Search results for "Linear"

showing 10 items of 7165 documents

Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory

2006

To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning's hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to impro…

Coupled clusterBasis (linear algebra)Mean squared errorQuantum mechanicsCardinal numberReference data (financial markets)ExtrapolationGeneral Physics and AstronomyApplied mathematicsLimit (mathematics)Physical and Theoretical ChemistryBasis setMathematicsThe Journal of Chemical Physics
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Linear-response theory for Mukherjee's multireference coupled-cluster method: Excitation energies

2012

The recently presented linear-response function for Mukherjee's multireference coupled-cluster method (Mk-MRCC) [T.-C. Jagau and J. Gauss, J. Chem. Phys. 137, 044115 (2012)] is employed to determine vertical excitation energies within the singles and doubles approximation (Mk-MRCCSD-LR) for ozone as well as for o-benzyne, m-benzyne, and p-benzyne, which display increasing multireference character in their ground states. In order to assess the impact of a multireference ground-state wavefunction on excitation energies, we compare all our results to those obtained at the single-reference coupled-cluster level of theory within the singles and doubles as well as within the singles, doubles, and…

Coupled clusterChemistryQuantum mechanicsExcited stateGaussGeneral Physics and AstronomyPhysical and Theoretical ChemistryWave functionLinear response theoryExcitationThe Journal of Chemical Physics
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Implementation of transition moments between excited states in the approximate coupled-cluster singles and doubles model

2008

An implementation of transition moments between excited states for the approximate coupled-cluster singles and doubles model (CC2) using the resolution of the identity (RI) approximation is reported. The accuracy of the RI approximation is analyzed for a testset of 7 molecules and 76 transitions. The RI error is found to be very small for both transition moments and oscillator strengths. Furthermore, the performance of the CC2 model in comparison with coupled-cluster singles and doubles (CCSD) is studied for 40 transitions of the same testset, yielding deviations of about 12% for the transition moments and 24% for the oscillator strengths. In addition, for 13 transitions of the testset the …

Coupled clusterDegree (graph theory)Basis (linear algebra)ChemistryExcited stateResolution (electron density)General Physics and AstronomyPhysical and Theoretical ChemistryTriplet stateAtomic physicsGround stateSpectral lineThe Journal of Chemical Physics
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Molecular equilibrium geometries based on coupled-cluster calculations including quadruple excitations

2005

Using analytic gradient techniques and an additivity scheme for the various electron correlation contributions, i.e. core-correlation, contribution due to full treatment of triple excitations and contributions due to quadruple excitations calculated with different basis sets, the accuracy of computed geometrical parameters are analysed in comparison with experiment. For a test set of 12 closed-shell and 5 open-shell molecules, it is found that inclusion of quadruple excitations is essential to reach agreement with experiment. The mean error of 0.002 pm and the standard deviation of 0.040 pm of the present CCSD(T)/cc-pV6Z + core(CCSD(T)/cc-pCVQZ) + T/cc-pVTZ + Q/cc-pVDZ results for the close…

Coupled clusterElectronic correlationMean squared errorBasis (linear algebra)ChemistryAdditive functionBiophysicsMoleculePhysical and Theoretical ChemistryAtomic physicsCondensed Matter PhysicsMolecular BiologyStandard deviationMolecular Physics
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Analytic gradients for Mukherjee’s multireference coupled-cluster method using two-configurational self-consistent-field orbitals

2010

Analytic gradients for the state-specific multireference coupled-cluster method suggested by Mahapatra et al. [Mol. Phys. 94, 157 (1998)] (Mk-MRCC) are reported within the singles and doubles approximation using two-configurational self-consistent field (TCSCF) orbitals. The present implementation extends our previous work on Mk-MRCC gradients [E. Prochnow et al., J. Chem. Phys. 131, 064109 (2009)] which is based on restricted Hartree-Fock orbitals and consequently the main focus of the present paper is on the treatment of orbital relaxation at the TCSCF level using coupled-perturbed TCSCF theory. Geometry optimizations on m-arynes and nitrenes are presented to illustrate the influence of t…

Coupled clusterLinear combination of atomic orbitalsChemistryQuantum mechanicsRestricted open-shell Hartree–FockGeneral Physics and AstronomyMolecular orbital theoryMolecular orbitalComplete active spacePhysical and Theoretical ChemistrySlater-type orbitalBasis setThe Journal of Chemical Physics
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Pilot applications of internally contracted multireference coupled cluster theory, and how to choose the cluster operator properly.

2011

The internally contracted multireference coupled cluster (icMRCC) method allows a highly accurate description of both static and dynamic correlation with a computational scaling similar to single reference coupled cluster theory. The authors show that the method can lose its orbital invariance and size consistency when no special care is taken in the elimination of redundant excitations. Using the BeH(2) model system, four schemes are compared which differ in their treatment of linear dependencies between excitations of different rank (such as between singles and doubles). While the energy curves agree within tens of μE(h) when truncating the cluster operator at double excitations (icMRCCSD…

Coupled clusterRank (linear algebra)ChemistryOperator (physics)Cluster (physics)General Physics and AstronomySpecial careStatistical physicsPhysical and Theoretical ChemistryAtomic physicsSize consistency and size extensivityLinear combinationEnergy (signal processing)The Journal of chemical physics
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Importance of Triples Contributions to NMR Spin–Spin Coupling Constants Computed at the CC3 and CCSDT Levels

2016

We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin–spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1–3%, but much higher corrections were found for 1JCN in FCN, 15.7%, and 1JOF in OF2, 6.4%. The changes v…

Coupling constant010304 chemical physicsBasis (linear algebra)ChemistryNuclear magnetic resonance spectroscopy010402 general chemistry01 natural sciences0104 chemical sciencesComputer Science ApplicationsCoupled cluster0103 physical sciencesPhysical and Theoretical ChemistryAtomic physicsSpin-½Second derivativeJournal of Chemical Theory and Computation
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A Combined Experimental and Theoretical Study on the Magnetic Properties of a Family of Bis(μ‐phenoxido)dicopper(II) Complexes Bearing ω‐[Bis(2‐hydro…

2009

Five new neutral bis(μ-phenoxido)dicopper(II) complexes, [Cu2(μ-HL1)2]·3EtOH·H2O (1), [Cu2(μ-HL2)2]·1.65H2O (2), [Cu2(μ-HL3)2(μ-H2O)] (3), [Cu2(μ-HL4)2] (4) and [Cu2(μ-HL5)2(μ-H2O)] (5), were prepared from a family of ω-[bis(2-hydroxy-3,5-dimethylbenzyl)amino]alkan-1-ol ligands (H3L1–H3L5 derived from 2-aminoethanol, 3-aminopropanol, 4-aminobutanol, 5-aminopentanol and 6-aminohexanol, respectively) bearing a [O,N,O,O′] donor set. In complexes 3 and 5, there is also a bridging water molecule between the metallic centres. The copper(II) coordination planes of all these complexes form a roof-like structure (the bridging O atoms are located at the top of the roof). The structural differences fo…

Coupling constant010405 organic chemistryChemistryStereochemistrychemistry.chemical_element010402 general chemistry01 natural sciencesCopper0104 chemical sciencesMagnetic exchangeInorganic ChemistryMetalCrystallographyLinear relationshipFerromagnetismvisual_artvisual_art.visual_art_mediumAntiferromagnetismMoleculeEuropean Journal of Inorganic Chemistry
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H2 O, H2 , HF, F2 and F2 O nuclear magnetic shielding constants and indirect nuclear spin-spin coupling constants (SSCCs) in the BHandH/pcJ-n and BHa…

2009

Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H(2)O, H(2), HF, F(2) and F(2)O nuclear isotropic shielding constants in the BHandH Kohn-Sham basis set limit was shown. The results of two- and three-parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were mor…

Coupling constantBasis (linear algebra)ChemistryComputational chemistryAtomAb initioExtrapolationKohn–Sham equationsGeneral Materials ScienceGeneral ChemistryAtomic physicsSpin (physics)Basis setMagnetic Resonance in Chemistry
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Basis Set Convergence of Indirect Spin-Spin Coupling Constants in the Kohn-Sham Limit for Several Small Molecules

2012

The performance of more than 40 density functionals in predicting indirect spin-spin coupling constants (SSCCs) in the Kohn-Sham basis set limit was tested. For comparison, similar calculations were performed using the RHF, SOPPA, SOPPA(CC2), and SOPPA(CCSD) methods, and the results were estimated toward the complete basis set (CBS) limit. The SSCCs of nine small molecules (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6), and C(6)H(6)) were calculated using the dedicated Jensen pcJ-n polarization-consistent basis sets and used for the CBS limit estimations within the Kohn-Sham limit. These CBS results were compared with calculations using the aug-cc-pVTZ-J basis set. Among the 4…

Coupling constantBasis (linear algebra)Computational chemistryChemistryConvergence (routing)Kohn–Sham equationsLimit (mathematics)Physical and Theoretical ChemistryMolecular physicsSmall moleculeBasis setSpin-½
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